“RF engineering is often regarded as the black magic of electronics. It may be a strange combination of mathematics and mechanics, sometimes even just trial and error. It has puzzled many outstanding engineers, and some engineers only know the results without knowing the details.
Complex mixer, zero-IF architecture and advanced algorithm development
RF engineering is often regarded as the black magic of electronics. It may be a strange combination of mathematics and mechanics, sometimes even just trial and error. It has puzzled many outstanding engineers, and some engineers only know the results without knowing the details.
There is an interesting connection between complex mixers, zero-IF architectures, and advanced algorithm development. This article aims to clarify the basic concepts of the above three, namely the working principle and the value they bring to the system design, and explain the interdependence between them.
RF engineering is often regarded as the black magic of electronics. It may be a strange combination of mathematics and mechanics, sometimes even just trial and error. It has puzzled many outstanding engineers, and some engineers only know the results without knowing the details. Many existing documents often do not establish basic concepts, but jump directly to theoretical and mathematical explanations.
Demystifying the Complex RF Mixer
Figure 1 is a schematic diagram of a complex mixer configured with an upconverter (transmitter). The two parallel paths each have independent mixers, and a common local oscillator feeds signals to these paths, and the phase of the local oscillator is 90° out of phase with one of the mixers. The two independent outputs are then summed in a summing amplifier to produce the required RF output.
Figure 1. Basic architecture of complex transmitter
This configuration has some simple but very useful applications. Suppose that only a signal tone is fed to the I input, and the Q input is not driven, as shown in Figure 2. Assuming that the audio frequency of the signal on the I input is x MHz, the mixer in the I path produces an output of LO frequency ±x. Since no signal is applied to the Q input, the spectrum produced by the mixer in this path is empty, and the output of the I mixer directly becomes the RF output.
Figure 2. I path analysis
Or, suppose that only one tone of frequency x is applied to the Q input. The Q mixer then generates an output whose signal tone is LO frequency ±x. Since no signal is applied to the I input, its mixer output is muted, and the output of the Q mixer becomes the RF output directly.
Figure 3. Q path analysis
At first glance, the output of Figure 2 and Figure 3 appear to be exactly the same. But in fact, there is a key difference between the two, and that is the phase. Assume that the same signal tone is applied to the I and Q inputs at the same time, and there is a 90° phase shift between the input channels, as shown in Figure 4.
Figure 4. Path analysis of simultaneous application of I and Q signals
Looking closely at the mixer output, we observe that the signal at the LO frequency plus the input frequency is in phase, but the signal at the LO frequency minus the input frequency is out of phase. This causes the tones on the upper side of the LO to add up, while the tones on the lower side cancel. Without any filtering, we eliminate one of the signal tones (or sidebands), and the resulting output is completely on one side of the LO frequency.
In the example shown in Figure 4, the I signal is 90° ahead of the Q signal. If the configuration is changed so that the Q signal is 90° ahead of the I signal, then similar addition and cancellation can be expected, but in this case, all signals will appear on the lower side of the LO.
Figure 5. The position of the signal tone depends on the phase relationship of I and Q
Figure 5 above shows the laboratory measurement results of a complex transmitter. Shown on the left is a test case where I is 90° ahead of Q, which causes the output signal tones to be located on the upper side of the LO. The right side of Figure 5 shows the opposite relationship, that is, Q is ahead of I by 90°, and the resulting output signal tone is located on the lower side of LO.
In theory, it should be possible to make all the energy fall on only one side of the LO. However, as shown in the laboratory measurement results in Figure 5, complete cancellation is impossible in practice, and some energy will remain on the other side of the LO. This is the so-called mirror image. It should also be noted that the energy of the LO frequency is also present, which is called LO leakage or LOL. You can also see other energies in the results-these are the harmonics of the desired signal and will not be discussed in this article.
In order to completely eliminate the image, the amplitude of the I and Q mixer outputs must be exactly the same, and the phase difference between each other on the LO image side is exactly 180°. If the above phase and amplitude requirements cannot be met, the addition/destruction process shown in Figure 4 will be less than ideal, and the energy of the image frequency will still exist.
When a conventional single-mixer architecture is used, LO± products are produced. One of the sidebands needs to be eliminated before transmission, usually by adding a bandpass filter. The roll-off frequency of the filter must be appropriate so that it can eliminate the unwanted image signal without affecting the desired signal.
Figure 6. Single mixer image filter requirements
The interval between the image and the desired signal will directly affect the requirements for the filter. If the interval is large, a simple, low-cost filter with a slower roll-off can be used. If the interval is narrow, the design must implement a filter with a steep response, usually a multi-pole or SAW filter. Therefore, it can be said that a proper interval must be maintained between the image and the desired signal so that the image can be filtered out without affecting the desired signal; this interval is inversely proportional to the complexity and cost of the filter. In addition, if the LO frequency is variable, the filter must be tunable, which will further increase the complexity of the filter.
The interval between the image and the desired signal is determined by the signal applied to the mixer. The example in Figure 6 shows a 10 MHz bandwidth signal that is 10 MHz away from DC. The corresponding mixer output places the image 20 MHz away from the desired signal. In this configuration, in order to achieve the required signal spectrum of 10 MHz at the output, a 20 MHz baseband signal path must be connected to the mixer. The baseband bandwidth of 10 MHz is not used, and the data interface rate of the mixer circuit is higher than necessary.
Returning to the complex mixer shown in Figure 5, we know that its architecture eliminates the image without the need for external filtering. Moreover, the efficiency can be optimized in the zero-IF architecture so that the signal path processing bandwidth is equal to the required signal bandwidth. The conceptual diagram shown in Figure 7 illustrates its implementation principle. As mentioned above, if I is ahead of Q by 90°, only the upper side of the LO will have an output. If Q is 90° ahead of I, only the lower side of LO will have output. Therefore, if two independent baseband signals are generated, one of which is designed to produce only the upper sideband output, the other is designed to produce only the lower sideband and the other is designed to produce only the lower sideband output, then they can be added in the baseband and applied to Multiple transmitters. The result will be that outputs with different signals appear on the upper and lower sides of the LO. In practical applications, the combined baseband signal is generated digitally. The summing node shown in Figure 7 is only to illustrate this concept.
Figure 7. Zero-IF complex mixer architecture
Zero IF bonus
Using a complex transmitter to produce a single sideband output has considerable advantages, and can reduce the RF filtering required to eliminate the image. However, if the image cancellation performance is good enough to make the image negligible, then the zero-IF mode can be used to further take advantage of the architecture. The zero intermediate frequency allows us to use specially created baseband data to generate RF output, thereby appearing independent signals on both sides of the LO. Figure 8 shows how this is achieved. We have two independent sets of I and Q data, encoded with symbol data, and the receiver can decode it according to the phase of the reference carrier.
Figure 8. An in-depth look at the I/Q signal in a zero-IF complex mixer configuration. Initial observations show that Q1 is 90° ahead of I1, and the amplitudes of the two are the same. Similarly, I2 is 90° ahead of Q2, and its amplitude is also the same. Combine these independent signals so that I1 + I2 = SumI1I2, and Q1 + Q2 = SumQ1Q2. The added I and Q signals no longer exhibit phase and amplitude correlation-their amplitudes are not equal at all times, and the phase relationship between the two is constantly changing. The resulting mixer output places I1/Q1 data on one side of the carrier and I2/Q2 data on the other side of the carrier, as described above and shown in Figure 7.
By placing independent data blocks adjacent to each other on either side of the LO, the zero intermediate frequency enhances the advantages of the complex transmitter. The data processing path bandwidth will never exceed the data bandwidth. Therefore, in theory, the use of a complex mixer in a zero-IF architecture provides a solution that does not require RF filtering, while optimizing baseband power efficiency and reducing the unit cost of unusable signal bandwidth.
So far, the focus of this article has been on the use of complex mixers as zero-IF transmitters. The same principle is also true in reverse, that is, the complex mixer architecture can be used as a zero-IF receiver. The advantages described for the transmitter also apply to the receiver. When using a single mixer to receive a signal, an RF mixer must first be used to filter out the image frequency. In the zero-IF working mode, there is no need to worry about the image frequency. The signal reception above the LO and the signal reception below the LO are independent of each other.
The complex receiver is shown in the figure below. The input spectrum is simultaneously applied to the I and Q mixers. One mixer is driven by LO and the other mixer is driven by LO + 90°. The output of the receiver is I and Q. For the receiver, it is not easy to prove from experience how the output corresponding to a given input will be, but if the input signal tone is higher than the LO, as shown in the figure, then the I and Q output will be at (signal tone C LO ) Frequency, and there will be a phase shift between I and Q (I leads Q). Similarly, if the input signal tone is lower than the LO, then the I and Q outputs are also at the (LO C signal tone) frequency, but this time Q is ahead of I. In this way, the complex receiver can distinguish between energy above the LO and energy below the LO.
The output of the complex receiver will be the sum of two types of I/Q information: one representing the received spectrum above the LO, and the other representing the received spectrum below the LO. This concept has been explained above for the complex transmitter, where the added I signal and the added Q signal are applied to the complex transmitter. For a complex receiver, the baseband processor that receives the added I information and the added Q information can use the complex FFT to easily distinguish between higher frequencies and lower frequencies.
Figure 9. Zero-IF complex mixer receiver configuration
When receiving the added I signal and the added Q signal, there are two known quantities-the added I signal and the added Q signal-but there are four unknowns, namely I1, Q1, I2, and Q2. Since there are more unknowns than knowns, it seems impossible to solve for I1, Q1, I2, and Q2. However, we also know that I1 = Q1 + 90, I2 = Q2 C 90. With these two known relationships, we can use the received I signal and the added Q signal to solve for I1, Q1, I2, and Q2. In fact, we only need to solve for I1 and I2, because the Q signal is a copy of the I signal, but the phase shift is only ±90.
In practice, complex mixers try to completely eliminate the image signal. This limitation has two prominent effects on the radio architecture design.
Even with performance limitations, multiple IFs can still bring tangible benefits. Consider the low-IF example shown in Figure 10. Due to performance limitations, we can indeed see mirroring. However, this image has been greatly attenuated compared to what was expected for a single-mixer design (see Figure 6). Although the complex mixer still needs a filter, the requirements on the filter can be relaxed a lot, and its implementation is simpler and lower in cost.
Figure 10. The actual implementation of the complex mixer pay attention to the attenuation image.
The filter complexity is inversely proportional to the distance between the image and the desired signal. If the zero-IF configuration is used, the distance will become 0 and the image will be in the desired signal band. The practical application of the zero-IF theory cannot be fully realized, and the resulting in-band image causes performance to drop to an unacceptable level (see Figure 11).
Figure 11. Limitations of zero-IF implementation
Only when the phase and amplitude requirements of the I and Q data paths are met, the principle of the complex transmitter and receiver can be established. The mismatch of the signal path will cause the image signals on both sides of the LO to not be accurately canceled. See Figure 10 and Figure 11 for examples of such problems. In the case of not using zero intermediate frequency, filtering can be used to eliminate the image. However, if the zero-IF architecture is used, the unwanted image will directly fall within the spectrum range of the desired signal. If the image power is large enough, a fault condition will occur. Therefore, only when the design can eliminate the inconsistency of the phase and amplitude on the signal path, the use of zero-IF and complex mixing can provide the optimal system design.
Advanced algorithm support
The concept of complex mixer architecture has existed for many years, but the challenge of meeting phase and amplitude requirements in a dynamic radio environment has limited its use in zero-IF mode. Analog Devices has overcome these challenges by using a combination of intelligent silicon chip design and advanced algorithms. The design allows for factors that affect the signal path, but the smart silicon design minimizes these effects. The remaining errors are eliminated by a self-optimizing quadrature error correction (QEC) algorithm. Figure 12 is a conceptual diagram.
Figure 12. Advanced QEC algorithm and smart silicon design support zero-IF architecture. On transceivers such as AD9371, the QEC algorithm is located in the on-chip ARM? processor. It continuously grasps the information of the silicon signal path, modulated RF output, input signal and external system environment, and uses this information to intelligently adapt the signal path profile in a controlled and predictive manner, rather than making an instinctive passive reaction. The performance of this algorithm is excellent, and it can be regarded as a digital aid to the analog signal path to achieve the best performance.
A variety of advanced algorithms reside and function inside the transceiver, and the dynamic QEC calibration algorithm is just one of the more prominent examples. Other coexisting algorithms include LO leakage elimination, etc. These algorithms improve the performance of the zero-IF architecture to the optimal level. Such first-generation transceiver algorithms are mainly used to support the implementation of related technologies, while second-generation algorithms (such as digital predistortion or DPD) can not only enhance the performance of the transceiver, but also improve the performance of the entire system.
All systems have some shortcomings that limit their performance. The first generation of algorithms mainly focused on eliminating on-chip limitations through calibration, while the new generation of algorithms uses intelligent means to eliminate system performance and efficiency constraints outside the transceiver, such as PA distortion and efficiency (DPD and CFR), duplexer performance (TxNc), Passive Intermodulation Problem (PIM), etc.
Complex mixers have existed for many years, but their image rejection performance does not allow them to be used in zero-IF mode. The combination of smart silicon design and advanced algorithms eliminates the performance barriers that previously prevented high-performance systems from adopting zero-IF architectures. After the performance limitation is eliminated, the use of a zero-IF architecture is beneficial to reducing filtering, power consumption, system complexity, size, heat, and weight.
For complex mixers and zero-IF, we can consider QEC and LOL algorithms as supporting functions. However, as the range of algorithm development expands, it brings a higher level of performance to system designers, enabling them to design radios more flexibly. They can choose enhanced performance or use the benefits of algorithms to reduce the cost or device size of the radio design.